Question

The graph represents y = 1/4x + 1/2














.



Which ordered pairs represent a point on the line and solutions to the equation? Select all that apply.

Responses
(3, 1)
(3, 1)
(0, 0.5)
(0, 0.5)
(0, -2)
(0, -2)
(-2, 0)
(-2, 0)
(2, 1)
(2, 1)
(6, 2)
(6, 2)
Skip to navigation

Answer 1

To determine which ordered pairs represent points on the line described by the equation \( y = \frac{1}{4}x + \frac{1}{2} \), we'll substitute each x-value in the ordered pairs and see if the resulting y-value matches the y-value in the pair.

1. For \( (3, 1) \):
\[
y = \frac{1}{4}(3) + \frac{1}{2} = \frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \quad \text{(not equal to 1)}
\]
Result: **Not on the line**

2. For \( (0, 0.5) \):
\[
y = \frac{1}{4}(0) + \frac{1}{2} = 0 + \frac{1}{2} = \frac{1}{2} \quad \text{(equal to 0.5)}
\]
Result: **On the line**

3. For \( (0, -2) \):
\[
y = \frac{1}{4}(0) + \frac{1}{2} = 0 + \frac{1}{2} = \frac{1}{2} \quad \text{(not equal to -2)}
\]
Result: **Not on the line**

4. For \( (-2, 0) \):
\[
y = \frac{1}{4}(-2) + \frac{1}{2} = -\frac{1}{2} + \frac{1}{2} = 0 \quad \text{(equal to 0)}
\]
Result: **On the line**

5. For \( (2, 1) \):
\[
y = \frac{1}{4}(2) + \frac{1}{2} = \frac{1}{2} + \frac{1}{2} = 1 \quad \text{(equal to 1)}
\]
Result: **On the line**

6. For \( (6, 2) \):
\[
y = \frac{1}{4}(6) + \frac{1}{2} = \frac{3}{2} + \frac{1}{2} = \frac{4}{2} = 2 \quad \text{(equal to 2)}
\]
Result: **On the line**

Based on the calculations, the ordered pairs that are on the line \( y = \frac{1}{4}x + \frac{1}{2} \) are:

- \( (0, 0.5) \)
- \( (-2, 0) \)
- \( (2, 1) \)
- \( (6, 2) \)

**Final Selected Ordered Pairs:**
- \( (0, 0.5) \)
- \( (-2, 0) \)
- \( (2, 1) \)
- \( (6, 2) \)